Properties

Label 252.6.k.e.37.2
Level $252$
Weight $6$
Character 252.37
Analytic conductor $40.417$
Analytic rank $0$
Dimension $4$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [252,6,Mod(37,252)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(252, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 2]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("252.37");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 252.k (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(40.4167225929\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{7081})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} + 1771x^{2} + 1770x + 3132900 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 84)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 37.2
Root \(-20.7872 + 36.0044i\) of defining polynomial
Character \(\chi\) \(=\) 252.37
Dual form 252.6.k.e.109.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(32.7872 - 56.7890i) q^{5} +(40.6487 - 123.104i) q^{7} +O(q^{10})\) \(q+(32.7872 - 56.7890i) q^{5} +(40.6487 - 123.104i) q^{7} +(-122.787 - 212.674i) q^{11} +434.872 q^{13} +(-551.149 - 954.618i) q^{17} +(1438.65 - 2491.81i) q^{19} +(-2114.72 + 3662.80i) q^{23} +(-587.497 - 1017.57i) q^{25} -4969.60 q^{29} +(4391.32 + 7606.00i) q^{31} +(-5658.22 - 6344.64i) q^{35} +(1220.03 - 2113.15i) q^{37} +3668.55 q^{41} -7198.06 q^{43} +(1636.66 - 2834.78i) q^{47} +(-13502.4 - 10008.1i) q^{49} +(-1510.84 - 2616.84i) q^{53} -16103.4 q^{55} +(-25743.7 - 44589.5i) q^{59} +(6656.65 - 11529.6i) q^{61} +(14258.2 - 24695.9i) q^{65} +(-15447.9 - 26756.5i) q^{67} +41882.8 q^{71} +(-17308.7 - 29979.5i) q^{73} +(-31172.2 + 6470.74i) q^{77} +(-38771.7 + 67154.6i) q^{79} -100908. q^{83} -72282.4 q^{85} +(20391.8 - 35319.7i) q^{89} +(17677.0 - 53534.6i) q^{91} +(-94338.2 - 163399. i) q^{95} +140147. q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 47 q^{5} - 174 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 47 q^{5} - 174 q^{7} - 407 q^{11} + 898 q^{13} - 1868 q^{17} + 1463 q^{19} - 44 q^{23} + 1605 q^{25} - 1534 q^{29} + 11170 q^{31} - 9674 q^{35} + 3113 q^{37} + 15684 q^{41} - 25258 q^{43} + 9576 q^{47} + 4558 q^{49} + 13395 q^{53} - 26210 q^{55} - 47521 q^{59} + 63652 q^{61} + 28254 q^{65} - 44541 q^{67} + 251680 q^{71} - 6039 q^{73} - 35407 q^{77} - 17588 q^{79} - 78650 q^{83} - 116120 q^{85} + 83082 q^{89} + 31747 q^{91} - 214946 q^{95} + 369570 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) 32.7872 56.7890i 0.586515 1.01587i −0.408170 0.912906i \(-0.633833\pi\)
0.994685 0.102967i \(-0.0328337\pi\)
\(6\) 0 0
\(7\) 40.6487 123.104i 0.313546 0.949573i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −122.787 212.674i −0.305965 0.529946i 0.671511 0.740995i \(-0.265646\pi\)
−0.977476 + 0.211048i \(0.932312\pi\)
\(12\) 0 0
\(13\) 434.872 0.713679 0.356839 0.934166i \(-0.383854\pi\)
0.356839 + 0.934166i \(0.383854\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −551.149 954.618i −0.462537 0.801138i 0.536550 0.843869i \(-0.319727\pi\)
−0.999087 + 0.0427312i \(0.986394\pi\)
\(18\) 0 0
\(19\) 1438.65 2491.81i 0.914260 1.58355i 0.106279 0.994336i \(-0.466106\pi\)
0.807981 0.589209i \(-0.200560\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −2114.72 + 3662.80i −0.833552 + 1.44375i 0.0616521 + 0.998098i \(0.480363\pi\)
−0.895204 + 0.445657i \(0.852970\pi\)
\(24\) 0 0
\(25\) −587.497 1017.57i −0.187999 0.325624i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −4969.60 −1.09730 −0.548652 0.836051i \(-0.684859\pi\)
−0.548652 + 0.836051i \(0.684859\pi\)
\(30\) 0 0
\(31\) 4391.32 + 7606.00i 0.820713 + 1.42152i 0.905152 + 0.425088i \(0.139757\pi\)
−0.0844390 + 0.996429i \(0.526910\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −5658.22 6344.64i −0.780746 0.875462i
\(36\) 0 0
\(37\) 1220.03 2113.15i 0.146510 0.253762i −0.783425 0.621486i \(-0.786529\pi\)
0.929935 + 0.367723i \(0.119863\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 3668.55 0.340828 0.170414 0.985373i \(-0.445489\pi\)
0.170414 + 0.985373i \(0.445489\pi\)
\(42\) 0 0
\(43\) −7198.06 −0.593669 −0.296835 0.954929i \(-0.595931\pi\)
−0.296835 + 0.954929i \(0.595931\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 1636.66 2834.78i 0.108072 0.187187i −0.806917 0.590665i \(-0.798866\pi\)
0.914989 + 0.403478i \(0.132199\pi\)
\(48\) 0 0
\(49\) −13502.4 10008.1i −0.803378 0.595470i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −1510.84 2616.84i −0.0738801 0.127964i 0.826719 0.562616i \(-0.190205\pi\)
−0.900599 + 0.434651i \(0.856872\pi\)
\(54\) 0 0
\(55\) −16103.4 −0.717811
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −25743.7 44589.5i −0.962812 1.66764i −0.715381 0.698735i \(-0.753747\pi\)
−0.247432 0.968905i \(-0.579587\pi\)
\(60\) 0 0
\(61\) 6656.65 11529.6i 0.229050 0.396727i −0.728477 0.685071i \(-0.759771\pi\)
0.957527 + 0.288344i \(0.0931046\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 14258.2 24695.9i 0.418583 0.725007i
\(66\) 0 0
\(67\) −15447.9 26756.5i −0.420418 0.728186i 0.575562 0.817758i \(-0.304783\pi\)
−0.995980 + 0.0895723i \(0.971450\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 41882.8 0.986030 0.493015 0.870021i \(-0.335895\pi\)
0.493015 + 0.870021i \(0.335895\pi\)
\(72\) 0 0
\(73\) −17308.7 29979.5i −0.380151 0.658441i 0.610932 0.791683i \(-0.290795\pi\)
−0.991084 + 0.133242i \(0.957461\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −31172.2 + 6470.74i −0.599157 + 0.124373i
\(78\) 0 0
\(79\) −38771.7 + 67154.6i −0.698952 + 1.21062i 0.269878 + 0.962895i \(0.413017\pi\)
−0.968830 + 0.247726i \(0.920317\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −100908. −1.60779 −0.803897 0.594768i \(-0.797244\pi\)
−0.803897 + 0.594768i \(0.797244\pi\)
\(84\) 0 0
\(85\) −72282.4 −1.08514
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 20391.8 35319.7i 0.272886 0.472652i −0.696714 0.717349i \(-0.745355\pi\)
0.969600 + 0.244697i \(0.0786885\pi\)
\(90\) 0 0
\(91\) 17677.0 53534.6i 0.223771 0.677690i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −94338.2 163399.i −1.07245 1.85755i
\(96\) 0 0
\(97\) 140147. 1.51236 0.756178 0.654366i \(-0.227064\pi\)
0.756178 + 0.654366i \(0.227064\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 4288.23 + 7427.43i 0.0418287 + 0.0724494i 0.886182 0.463338i \(-0.153348\pi\)
−0.844353 + 0.535787i \(0.820015\pi\)
\(102\) 0 0
\(103\) 17630.1 30536.2i 0.163742 0.283610i −0.772466 0.635057i \(-0.780977\pi\)
0.936208 + 0.351447i \(0.114310\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −96314.3 + 166821.i −0.813264 + 1.40861i 0.0973041 + 0.995255i \(0.468978\pi\)
−0.910568 + 0.413360i \(0.864355\pi\)
\(108\) 0 0
\(109\) −61646.1 106774.i −0.496980 0.860795i 0.503014 0.864279i \(-0.332225\pi\)
−0.999994 + 0.00348322i \(0.998891\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −28400.9 −0.209236 −0.104618 0.994512i \(-0.533362\pi\)
−0.104618 + 0.994512i \(0.533362\pi\)
\(114\) 0 0
\(115\) 138671. + 240186.i 0.977781 + 1.69357i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −139921. + 29044.9i −0.905765 + 0.188019i
\(120\) 0 0
\(121\) 50372.1 87247.1i 0.312771 0.541736i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 127870. 0.731973
\(126\) 0 0
\(127\) −47198.8 −0.259670 −0.129835 0.991536i \(-0.541445\pi\)
−0.129835 + 0.991536i \(0.541445\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 39904.7 69116.9i 0.203163 0.351889i −0.746383 0.665517i \(-0.768211\pi\)
0.949546 + 0.313628i \(0.101544\pi\)
\(132\) 0 0
\(133\) −248273. 278392.i −1.21703 1.36467i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −43032.1 74533.9i −0.195881 0.339275i 0.751308 0.659952i \(-0.229423\pi\)
−0.947189 + 0.320676i \(0.896090\pi\)
\(138\) 0 0
\(139\) 270587. 1.18787 0.593935 0.804513i \(-0.297573\pi\)
0.593935 + 0.804513i \(0.297573\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −53396.7 92485.7i −0.218360 0.378211i
\(144\) 0 0
\(145\) −162939. + 282219.i −0.643585 + 1.11472i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −86273.9 + 149431.i −0.318356 + 0.551410i −0.980145 0.198281i \(-0.936464\pi\)
0.661789 + 0.749690i \(0.269798\pi\)
\(150\) 0 0
\(151\) 8949.75 + 15501.4i 0.0319425 + 0.0553260i 0.881555 0.472082i \(-0.156497\pi\)
−0.849612 + 0.527408i \(0.823164\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 575916. 1.92544
\(156\) 0 0
\(157\) 89509.3 + 155035.i 0.289814 + 0.501972i 0.973765 0.227555i \(-0.0730733\pi\)
−0.683951 + 0.729528i \(0.739740\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 364946. + 409219.i 1.10959 + 1.24420i
\(162\) 0 0
\(163\) 118645. 205498.i 0.349767 0.605814i −0.636441 0.771325i \(-0.719594\pi\)
0.986208 + 0.165511i \(0.0529275\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 94040.0 0.260928 0.130464 0.991453i \(-0.458353\pi\)
0.130464 + 0.991453i \(0.458353\pi\)
\(168\) 0 0
\(169\) −182180. −0.490663
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 244357. 423238.i 0.620739 1.07515i −0.368609 0.929584i \(-0.620166\pi\)
0.989348 0.145567i \(-0.0465006\pi\)
\(174\) 0 0
\(175\) −149149. + 30960.4i −0.368150 + 0.0764207i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 406498. + 704075.i 0.948257 + 1.64243i 0.749095 + 0.662462i \(0.230488\pi\)
0.199161 + 0.979967i \(0.436178\pi\)
\(180\) 0 0
\(181\) −332961. −0.755434 −0.377717 0.925921i \(-0.623291\pi\)
−0.377717 + 0.925921i \(0.623291\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −80002.7 138569.i −0.171860 0.297671i
\(186\) 0 0
\(187\) −135348. + 234430.i −0.283040 + 0.490240i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −72143.9 + 124957.i −0.143092 + 0.247843i −0.928660 0.370933i \(-0.879038\pi\)
0.785567 + 0.618776i \(0.212371\pi\)
\(192\) 0 0
\(193\) 447310. + 774763.i 0.864400 + 1.49719i 0.867641 + 0.497190i \(0.165635\pi\)
−0.00324119 + 0.999995i \(0.501032\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 599462. 1.10052 0.550258 0.834995i \(-0.314530\pi\)
0.550258 + 0.834995i \(0.314530\pi\)
\(198\) 0 0
\(199\) 389129. + 673992.i 0.696564 + 1.20648i 0.969651 + 0.244495i \(0.0786222\pi\)
−0.273086 + 0.961990i \(0.588044\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −202008. + 611780.i −0.344055 + 1.04197i
\(204\) 0 0
\(205\) 120282. 208334.i 0.199901 0.346238i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −706589. −1.11893
\(210\) 0 0
\(211\) −810532. −1.25333 −0.626663 0.779291i \(-0.715580\pi\)
−0.626663 + 0.779291i \(0.715580\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −236004. + 408771.i −0.348196 + 0.603093i
\(216\) 0 0
\(217\) 1.11483e6 231418.i 1.60717 0.333616i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −239679. 415136.i −0.330103 0.571755i
\(222\) 0 0
\(223\) 220486. 0.296905 0.148453 0.988920i \(-0.452571\pi\)
0.148453 + 0.988920i \(0.452571\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 671890. + 1.16375e6i 0.865433 + 1.49897i 0.866617 + 0.498974i \(0.166290\pi\)
−0.00118391 + 0.999999i \(0.500377\pi\)
\(228\) 0 0
\(229\) 521292. 902904.i 0.656889 1.13777i −0.324528 0.945876i \(-0.605205\pi\)
0.981417 0.191889i \(-0.0614614\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 316256. 547771.i 0.381635 0.661011i −0.609661 0.792662i \(-0.708694\pi\)
0.991296 + 0.131651i \(0.0420278\pi\)
\(234\) 0 0
\(235\) −107323. 185889.i −0.126772 0.219575i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 684919. 0.775612 0.387806 0.921741i \(-0.373233\pi\)
0.387806 + 0.921741i \(0.373233\pi\)
\(240\) 0 0
\(241\) 3866.44 + 6696.87i 0.00428814 + 0.00742728i 0.868162 0.496282i \(-0.165302\pi\)
−0.863873 + 0.503709i \(0.831968\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −1.01105e6 + 438651.i −1.07611 + 0.466878i
\(246\) 0 0
\(247\) 625626. 1.08362e6i 0.652488 1.13014i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −1.09614e6 −1.09820 −0.549098 0.835758i \(-0.685029\pi\)
−0.549098 + 0.835758i \(0.685029\pi\)
\(252\) 0 0
\(253\) 1.03864e6 1.02015
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 357460. 619139.i 0.337594 0.584730i −0.646386 0.763011i \(-0.723720\pi\)
0.983980 + 0.178281i \(0.0570536\pi\)
\(258\) 0 0
\(259\) −210546. 236088.i −0.195028 0.218688i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −298256. 516595.i −0.265889 0.460533i 0.701907 0.712268i \(-0.252332\pi\)
−0.967796 + 0.251735i \(0.918999\pi\)
\(264\) 0 0
\(265\) −198144. −0.173327
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −1.01654e6 1.76070e6i −0.856531 1.48356i −0.875217 0.483730i \(-0.839282\pi\)
0.0186864 0.999825i \(-0.494052\pi\)
\(270\) 0 0
\(271\) −897277. + 1.55413e6i −0.742170 + 1.28548i 0.209336 + 0.977844i \(0.432870\pi\)
−0.951505 + 0.307632i \(0.900463\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −144274. + 249890.i −0.115042 + 0.199259i
\(276\) 0 0
\(277\) −211790. 366831.i −0.165846 0.287254i 0.771109 0.636703i \(-0.219702\pi\)
−0.936956 + 0.349449i \(0.886369\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 1.63799e6 1.23750 0.618749 0.785589i \(-0.287640\pi\)
0.618749 + 0.785589i \(0.287640\pi\)
\(282\) 0 0
\(283\) 147018. + 254642.i 0.109120 + 0.189001i 0.915414 0.402514i \(-0.131863\pi\)
−0.806294 + 0.591515i \(0.798530\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 149122. 451615.i 0.106865 0.323641i
\(288\) 0 0
\(289\) 102399. 177360.i 0.0721191 0.124914i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 356961. 0.242913 0.121457 0.992597i \(-0.461243\pi\)
0.121457 + 0.992597i \(0.461243\pi\)
\(294\) 0 0
\(295\) −3.37626e6 −2.25881
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −919631. + 1.59285e6i −0.594888 + 1.03038i
\(300\) 0 0
\(301\) −292592. + 886113.i −0.186143 + 0.563732i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −436505. 756049.i −0.268683 0.465372i
\(306\) 0 0
\(307\) −2.04097e6 −1.23592 −0.617960 0.786210i \(-0.712041\pi\)
−0.617960 + 0.786210i \(0.712041\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 1.02337e6 + 1.77253e6i 0.599972 + 1.03918i 0.992824 + 0.119581i \(0.0381552\pi\)
−0.392852 + 0.919602i \(0.628512\pi\)
\(312\) 0 0
\(313\) −319272. + 552996.i −0.184205 + 0.319052i −0.943308 0.331918i \(-0.892304\pi\)
0.759104 + 0.650970i \(0.225638\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 1.74954e6 3.03030e6i 0.977860 1.69370i 0.307705 0.951482i \(-0.400439\pi\)
0.670155 0.742221i \(-0.266228\pi\)
\(318\) 0 0
\(319\) 610203. + 1.05690e6i 0.335736 + 0.581512i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −3.17163e6 −1.69152
\(324\) 0 0
\(325\) −255486. 442514.i −0.134171 0.232391i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −282446. 316710.i −0.143862 0.161314i
\(330\) 0 0
\(331\) 1.47089e6 2.54766e6i 0.737923 1.27812i −0.215506 0.976503i \(-0.569140\pi\)
0.953429 0.301618i \(-0.0975266\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −2.02597e6 −0.986326
\(336\) 0 0
\(337\) 2.77854e6 1.33273 0.666364 0.745627i \(-0.267850\pi\)
0.666364 + 0.745627i \(0.267850\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 1.07840e6 1.86784e6i 0.502218 0.869868i
\(342\) 0 0
\(343\) −1.78089e6 + 1.25539e6i −0.817338 + 0.576159i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −86001.9 148960.i −0.0383429 0.0664118i 0.846217 0.532838i \(-0.178875\pi\)
−0.884560 + 0.466426i \(0.845541\pi\)
\(348\) 0 0
\(349\) −3.88321e6 −1.70658 −0.853290 0.521436i \(-0.825397\pi\)
−0.853290 + 0.521436i \(0.825397\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −385467. 667649.i −0.164646 0.285175i 0.771884 0.635764i \(-0.219315\pi\)
−0.936529 + 0.350589i \(0.885981\pi\)
\(354\) 0 0
\(355\) 1.37322e6 2.37849e6i 0.578321 1.00168i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 1.57017e6 2.71961e6i 0.642998 1.11370i −0.341763 0.939786i \(-0.611024\pi\)
0.984760 0.173918i \(-0.0556428\pi\)
\(360\) 0 0
\(361\) −2.90135e6 5.02529e6i −1.17174 2.02952i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −2.27001e6 −0.891857
\(366\) 0 0
\(367\) 182842. + 316691.i 0.0708615 + 0.122736i 0.899279 0.437375i \(-0.144092\pi\)
−0.828418 + 0.560111i \(0.810758\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −383559. + 79619.2i −0.144676 + 0.0300319i
\(372\) 0 0
\(373\) 77129.9 133593.i 0.0287045 0.0497177i −0.851316 0.524653i \(-0.824195\pi\)
0.880021 + 0.474935i \(0.157528\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −2.16114e6 −0.783122
\(378\) 0 0
\(379\) 4.06013e6 1.45192 0.725959 0.687738i \(-0.241396\pi\)
0.725959 + 0.687738i \(0.241396\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 1.02152e6 1.76932e6i 0.355834 0.616323i −0.631426 0.775436i \(-0.717530\pi\)
0.987260 + 0.159113i \(0.0508633\pi\)
\(384\) 0 0
\(385\) −654581. + 1.98240e6i −0.225067 + 0.681614i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −1.06183e6 1.83915e6i −0.355780 0.616229i 0.631471 0.775399i \(-0.282451\pi\)
−0.987251 + 0.159170i \(0.949118\pi\)
\(390\) 0 0
\(391\) 4.66209e6 1.54219
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 2.54243e6 + 4.40362e6i 0.819892 + 1.42009i
\(396\) 0 0
\(397\) 1.83182e6 3.17280e6i 0.583319 1.01034i −0.411764 0.911291i \(-0.635087\pi\)
0.995083 0.0990473i \(-0.0315795\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −32044.9 + 55503.3i −0.00995170 + 0.0172369i −0.870958 0.491357i \(-0.836501\pi\)
0.861007 + 0.508594i \(0.169834\pi\)
\(402\) 0 0
\(403\) 1.90966e6 + 3.30763e6i 0.585725 + 1.01451i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −599216. −0.179307
\(408\) 0 0
\(409\) −1.01287e6 1.75434e6i −0.299395 0.518568i 0.676603 0.736348i \(-0.263452\pi\)
−0.975998 + 0.217781i \(0.930118\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −6.53561e6 + 1.35666e6i −1.88543 + 0.391379i
\(414\) 0 0
\(415\) −3.30849e6 + 5.73047e6i −0.942995 + 1.63332i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −2.38986e6 −0.665025 −0.332513 0.943099i \(-0.607896\pi\)
−0.332513 + 0.943099i \(0.607896\pi\)
\(420\) 0 0
\(421\) 3.46875e6 0.953822 0.476911 0.878952i \(-0.341756\pi\)
0.476911 + 0.878952i \(0.341756\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −647596. + 1.12167e6i −0.173913 + 0.301226i
\(426\) 0 0
\(427\) −1.14877e6 1.28813e6i −0.304903 0.341892i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −802201. 1.38945e6i −0.208013 0.360289i 0.743076 0.669207i \(-0.233366\pi\)
−0.951088 + 0.308919i \(0.900033\pi\)
\(432\) 0 0
\(433\) 741661. 0.190102 0.0950508 0.995472i \(-0.469699\pi\)
0.0950508 + 0.995472i \(0.469699\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 6.08466e6 + 1.05389e7i 1.52417 + 2.63993i
\(438\) 0 0
\(439\) −1.43394e6 + 2.48365e6i −0.355115 + 0.615077i −0.987138 0.159873i \(-0.948892\pi\)
0.632023 + 0.774950i \(0.282225\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −89148.9 + 154410.i −0.0215827 + 0.0373824i −0.876615 0.481192i \(-0.840204\pi\)
0.855032 + 0.518575i \(0.173537\pi\)
\(444\) 0 0
\(445\) −1.33718e6 2.31607e6i −0.320103 0.554435i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 2.77890e6 0.650515 0.325258 0.945625i \(-0.394549\pi\)
0.325258 + 0.945625i \(0.394549\pi\)
\(450\) 0 0
\(451\) −450451. 780205.i −0.104281 0.180621i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −2.46060e6 2.75911e6i −0.557202 0.624798i
\(456\) 0 0
\(457\) −3.20669e6 + 5.55416e6i −0.718236 + 1.24402i 0.243462 + 0.969910i \(0.421717\pi\)
−0.961698 + 0.274111i \(0.911617\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 6.88393e6 1.50864 0.754318 0.656510i \(-0.227968\pi\)
0.754318 + 0.656510i \(0.227968\pi\)
\(462\) 0 0
\(463\) 6.70530e6 1.45367 0.726835 0.686812i \(-0.240991\pi\)
0.726835 + 0.686812i \(0.240991\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −1.62836e6 + 2.82041e6i −0.345509 + 0.598439i −0.985446 0.169988i \(-0.945627\pi\)
0.639937 + 0.768427i \(0.278960\pi\)
\(468\) 0 0
\(469\) −3.92178e6 + 814084.i −0.823286 + 0.170898i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 883830. + 1.53084e6i 0.181642 + 0.314613i
\(474\) 0 0
\(475\) −3.38080e6 −0.687520
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 4.67916e6 + 8.10454e6i 0.931814 + 1.61395i 0.780219 + 0.625506i \(0.215108\pi\)
0.151595 + 0.988443i \(0.451559\pi\)
\(480\) 0 0
\(481\) 530557. 918951.i 0.104561 0.181105i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 4.59502e6 7.95881e6i 0.887019 1.53636i
\(486\) 0 0
\(487\) 1.31470e6 + 2.27712e6i 0.251191 + 0.435075i 0.963854 0.266431i \(-0.0858445\pi\)
−0.712663 + 0.701506i \(0.752511\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 4.81856e6 0.902015 0.451008 0.892520i \(-0.351065\pi\)
0.451008 + 0.892520i \(0.351065\pi\)
\(492\) 0 0
\(493\) 2.73899e6 + 4.74407e6i 0.507543 + 0.879091i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 1.70248e6 5.15596e6i 0.309166 0.936308i
\(498\) 0 0
\(499\) 2.09549e6 3.62949e6i 0.376733 0.652521i −0.613851 0.789422i \(-0.710381\pi\)
0.990585 + 0.136900i \(0.0437139\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 1.75338e6 0.308999 0.154500 0.987993i \(-0.450623\pi\)
0.154500 + 0.987993i \(0.450623\pi\)
\(504\) 0 0
\(505\) 562395. 0.0981326
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 2.80923e6 4.86573e6i 0.480610 0.832441i −0.519142 0.854688i \(-0.673749\pi\)
0.999753 + 0.0222464i \(0.00708185\pi\)
\(510\) 0 0
\(511\) −4.39418e6 + 912146.i −0.744433 + 0.154530i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −1.15608e6 2.00239e6i −0.192075 0.332683i
\(516\) 0 0
\(517\) −803844. −0.132265
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 5.53589e6 + 9.58845e6i 0.893498 + 1.54758i 0.835653 + 0.549258i \(0.185089\pi\)
0.0578446 + 0.998326i \(0.481577\pi\)
\(522\) 0 0
\(523\) 3.79894e6 6.57996e6i 0.607307 1.05189i −0.384375 0.923177i \(-0.625583\pi\)
0.991682 0.128710i \(-0.0410836\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 4.84055e6 8.38407e6i 0.759220 1.31501i
\(528\) 0 0
\(529\) −5.72588e6 9.91752e6i −0.889618 1.54086i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 1.59535e6 0.243242
\(534\) 0 0
\(535\) 6.31575e6 + 1.09392e7i 0.953982 + 1.65235i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −470532. + 4.10046e6i −0.0697618 + 0.607940i
\(540\) 0 0
\(541\) 1.67539e6 2.90187e6i 0.246107 0.426270i −0.716335 0.697756i \(-0.754182\pi\)
0.962442 + 0.271486i \(0.0875152\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −8.08480e6 −1.16595
\(546\) 0 0
\(547\) −1.00856e7 −1.44123 −0.720615 0.693335i \(-0.756140\pi\)
−0.720615 + 0.693335i \(0.756140\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −7.14950e6 + 1.23833e7i −1.00322 + 1.73763i
\(552\) 0 0
\(553\) 6.69101e6 + 7.50272e6i 0.930419 + 1.04329i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 6.78337e6 + 1.17491e7i 0.926419 + 1.60460i 0.789263 + 0.614055i \(0.210463\pi\)
0.137155 + 0.990550i \(0.456204\pi\)
\(558\) 0 0
\(559\) −3.13023e6 −0.423689
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −1.98494e6 3.43802e6i −0.263922 0.457127i 0.703358 0.710835i \(-0.251683\pi\)
−0.967281 + 0.253708i \(0.918350\pi\)
\(564\) 0 0
\(565\) −931185. + 1.61286e6i −0.122720 + 0.212557i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −2.08724e6 + 3.61521e6i −0.270267 + 0.468116i −0.968930 0.247335i \(-0.920445\pi\)
0.698663 + 0.715451i \(0.253779\pi\)
\(570\) 0 0
\(571\) −1.92833e6 3.33996e6i −0.247509 0.428698i 0.715325 0.698792i \(-0.246279\pi\)
−0.962834 + 0.270094i \(0.912945\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 4.96956e6 0.626828
\(576\) 0 0
\(577\) 1.12288e6 + 1.94488e6i 0.140408 + 0.243194i 0.927650 0.373450i \(-0.121825\pi\)
−0.787242 + 0.616644i \(0.788492\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −4.10178e6 + 1.24222e7i −0.504118 + 1.52672i
\(582\) 0 0
\(583\) −371023. + 642630.i −0.0452094 + 0.0783050i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −6.40082e6 −0.766726 −0.383363 0.923598i \(-0.625234\pi\)
−0.383363 + 0.923598i \(0.625234\pi\)
\(588\) 0 0
\(589\) 2.52702e7 3.00138
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 5.56031e6 9.63074e6i 0.649325 1.12466i −0.333959 0.942588i \(-0.608385\pi\)
0.983284 0.182077i \(-0.0582820\pi\)
\(594\) 0 0
\(595\) −2.93818e6 + 8.89828e6i −0.340241 + 1.03042i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −6.56707e6 1.13745e7i −0.747833 1.29528i −0.948860 0.315698i \(-0.897761\pi\)
0.201027 0.979586i \(-0.435572\pi\)
\(600\) 0 0
\(601\) −7.88546e6 −0.890514 −0.445257 0.895403i \(-0.646888\pi\)
−0.445257 + 0.895403i \(0.646888\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −3.30312e6 5.72117e6i −0.366890 0.635472i
\(606\) 0 0
\(607\) 3.82967e6 6.63319e6i 0.421881 0.730719i −0.574243 0.818685i \(-0.694703\pi\)
0.996123 + 0.0879660i \(0.0280367\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 711738. 1.23277e6i 0.0771289 0.133591i
\(612\) 0 0
\(613\) 7.62066e6 + 1.31994e7i 0.819108 + 1.41874i 0.906340 + 0.422549i \(0.138864\pi\)
−0.0872322 + 0.996188i \(0.527802\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −1.35844e7 −1.43657 −0.718285 0.695749i \(-0.755073\pi\)
−0.718285 + 0.695749i \(0.755073\pi\)
\(618\) 0 0
\(619\) −3.18709e6 5.52019e6i −0.334324 0.579066i 0.649031 0.760762i \(-0.275175\pi\)
−0.983355 + 0.181696i \(0.941841\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −3.51911e6 3.94602e6i −0.363256 0.407323i
\(624\) 0 0
\(625\) 6.02844e6 1.04416e7i 0.617312 1.06922i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −2.68967e6 −0.271065
\(630\) 0 0
\(631\) −1.42736e7 −1.42712 −0.713561 0.700593i \(-0.752919\pi\)
−0.713561 + 0.700593i \(0.752919\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −1.54751e6 + 2.68037e6i −0.152300 + 0.263792i
\(636\) 0 0
\(637\) −5.87180e6 4.35222e6i −0.573354 0.424974i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −4.63480e6 8.02771e6i −0.445539 0.771697i 0.552550 0.833480i \(-0.313655\pi\)
−0.998090 + 0.0617828i \(0.980321\pi\)
\(642\) 0 0
\(643\) 1.17375e7 1.11956 0.559780 0.828641i \(-0.310885\pi\)
0.559780 + 0.828641i \(0.310885\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 5.12724e6 + 8.88063e6i 0.481529 + 0.834033i 0.999775 0.0211984i \(-0.00674818\pi\)
−0.518246 + 0.855232i \(0.673415\pi\)
\(648\) 0 0
\(649\) −6.32200e6 + 1.09500e7i −0.589173 + 1.02048i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 4.14489e6 7.17915e6i 0.380391 0.658856i −0.610727 0.791841i \(-0.709123\pi\)
0.991118 + 0.132985i \(0.0424562\pi\)
\(654\) 0 0
\(655\) −2.61672e6 4.53230e6i −0.238317 0.412776i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 2.06731e7 1.85435 0.927174 0.374631i \(-0.122230\pi\)
0.927174 + 0.374631i \(0.122230\pi\)
\(660\) 0 0
\(661\) −97171.2 168305.i −0.00865035 0.0149829i 0.861668 0.507473i \(-0.169420\pi\)
−0.870318 + 0.492490i \(0.836087\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −2.39498e7 + 4.97151e6i −2.10014 + 0.435948i
\(666\) 0 0
\(667\) 1.05093e7 1.82026e7i 0.914659 1.58424i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −3.26940e6 −0.280325
\(672\) 0 0
\(673\) −1.14437e7 −0.973929 −0.486965 0.873422i \(-0.661896\pi\)
−0.486965 + 0.873422i \(0.661896\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 4.51869e6 7.82660e6i 0.378914 0.656299i −0.611990 0.790865i \(-0.709631\pi\)
0.990905 + 0.134567i \(0.0429642\pi\)
\(678\) 0 0
\(679\) 5.69679e6 1.72527e7i 0.474193 1.43609i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −5.59212e6 9.68584e6i −0.458696 0.794485i 0.540196 0.841539i \(-0.318350\pi\)
−0.998892 + 0.0470541i \(0.985017\pi\)
\(684\) 0 0
\(685\) −5.64361e6 −0.459548
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −657020. 1.13799e6i −0.0527267 0.0913253i
\(690\) 0 0
\(691\) −2.83465e6 + 4.90976e6i −0.225842 + 0.391170i −0.956572 0.291497i \(-0.905847\pi\)
0.730730 + 0.682667i \(0.239180\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 8.87177e6 1.53664e7i 0.696704 1.20673i
\(696\) 0 0
\(697\) −2.02192e6 3.50207e6i −0.157646 0.273050i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 1.31822e6 0.101320 0.0506599 0.998716i \(-0.483868\pi\)
0.0506599 + 0.998716i \(0.483868\pi\)
\(702\) 0 0
\(703\) −3.51038e6 6.08016e6i −0.267896 0.464009i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 1.08866e6 225984.i 0.0819112 0.0170032i
\(708\) 0 0
\(709\) −4.13018e6 + 7.15368e6i −0.308570 + 0.534458i −0.978050 0.208372i \(-0.933184\pi\)
0.669480 + 0.742830i \(0.266517\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −3.71456e7 −2.73643
\(714\) 0 0
\(715\) −7.00290e6 −0.512287
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 1.13372e7 1.96365e7i 0.817865 1.41658i −0.0893870 0.995997i \(-0.528491\pi\)
0.907252 0.420587i \(-0.138176\pi\)
\(720\) 0 0
\(721\) −3.04250e6 3.41159e6i −0.217968 0.244410i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 2.91963e6 + 5.05694e6i 0.206292 + 0.357308i
\(726\) 0 0
\(727\) −1.93477e7 −1.35767 −0.678833 0.734293i \(-0.737514\pi\)
−0.678833 + 0.734293i \(0.737514\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 3.96720e6 + 6.87140e6i 0.274594 + 0.475611i
\(732\) 0 0
\(733\) −7.42922e6 + 1.28678e7i −0.510720 + 0.884593i 0.489203 + 0.872170i \(0.337288\pi\)
−0.999923 + 0.0124232i \(0.996045\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −3.79360e6 + 6.57071e6i −0.257266 + 0.445598i
\(738\) 0 0
\(739\) 8.84089e6 + 1.53129e7i 0.595504 + 1.03144i 0.993476 + 0.114045i \(0.0363810\pi\)
−0.397971 + 0.917398i \(0.630286\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 8.28756e6 0.550750 0.275375 0.961337i \(-0.411198\pi\)
0.275375 + 0.961337i \(0.411198\pi\)
\(744\) 0 0
\(745\) 5.65735e6 + 9.79882e6i 0.373442 + 0.646820i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 1.66214e7 + 1.86378e7i 1.08259 + 1.21392i
\(750\) 0 0
\(751\) 1.15682e7 2.00368e7i 0.748457 1.29637i −0.200104 0.979775i \(-0.564128\pi\)
0.948562 0.316592i \(-0.102539\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 1.17375e6 0.0749389
\(756\) 0 0
\(757\) −1.95475e7 −1.23980 −0.619900 0.784681i \(-0.712827\pi\)
−0.619900 + 0.784681i \(0.712827\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 3.91233e6 6.77635e6i 0.244891 0.424164i −0.717210 0.696857i \(-0.754581\pi\)
0.962101 + 0.272693i \(0.0879144\pi\)
\(762\) 0 0
\(763\) −1.56502e7 + 3.24867e6i −0.973214 + 0.202020i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −1.11952e7 1.93907e7i −0.687139 1.19016i
\(768\) 0 0
\(769\) −8.27325e6 −0.504499 −0.252250 0.967662i \(-0.581170\pi\)
−0.252250 + 0.967662i \(0.581170\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −9.41844e6 1.63132e7i −0.566931 0.981953i −0.996867 0.0790941i \(-0.974797\pi\)
0.429936 0.902859i \(-0.358536\pi\)
\(774\) 0 0
\(775\) 5.15978e6 8.93700e6i 0.308587 0.534488i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 5.27775e6 9.14133e6i 0.311605 0.539717i
\(780\) 0 0
\(781\) −5.14267e6 8.90737e6i −0.301690 0.522543i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 1.17390e7 0.679920
\(786\) 0 0
\(787\) 9.19734e6 + 1.59303e7i 0.529329 + 0.916824i 0.999415 + 0.0342037i \(0.0108895\pi\)
−0.470086 + 0.882621i \(0.655777\pi\)
\(788\) 0 0
\(789\)